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Properties of exponents

Last updated: 11 Nov 2008

Now for a look at some of the properties of exponents.

What does it mean to raise a number to the power of zero?

For example what is $mathematical expression$ ?

By definition we say that any number to the power of zero is equal to one. So,

$mathematical expression$

The only fractional exponents you will come across in the GMAT are $mathematical expression$ and $mathematical expression$ .

These correspond to square root and cube root respectively. For example,

$mathematical expression$

What does it mean to raise a number to the power of a negative number?

For example what is $mathematical expression$ ?

By definition we say that it is equal to the inverse (or reciprocal) of the positive power.

$mathematical expression$

Similarly

$mathematical expression$

Comments (3):

In the example of Cube root of 27, given by you on Fractional expoenents - Why can't the answer be +3 or -3.. Like in the case of Sq Rt of 16, provided by you as -4 or +4. ?

hrishikeshgmat on 14 Dec 2008 (permalink)
$mathematical expression$ so -3 is the cube root of -27 but not of 27.

joel on 14 Dec 2008 (permalink)
How would you express (4)with a -1/4 exponent?

iwkyle on 24 Feb 2010 (permalink)

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